Finding Initial Velocity from Rate, Distance, and Time

[bhoover05]

Hi guys! We started integral word problems today. I am very confused and could use some help with the following;

A particle is moving along a straight line accelerating at a constant rate of 5 m/s^2. Find the initial velocity if the particle moves 60m in the first 4 seconds.


Now, I have been able to do problems similar to these in the past, however without having an equation to start off with, I am confused to where I even begin.
t=4s
distance=60m
accelerating= 5 m/s^2
initial velocity=?

 

[jbunniii]

Can you start by writing an equation that expresses the velocity as a function of t? Call the initial velocity $v_0$ for now, since you don't know its value.

 

[hotvette]

Velocity is the time derivative of distance and acceleration is the time derivative of velocity. So, integrate the acceleration once with respect to time (and don't forget the beloved constant of integration) to get an expression for velocity and integrate velocity to get distance. That should give you enough to solve the problem.